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8:53 16:10 Suggested clip How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift YouTubeStart of suggested client of suggested clip How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift
The period is the distance between each repeating wave of the function, so from tip to tip of the function's graph. As you can see from this graph, the distance between the tips of the function is 3.034 – 1.463 = 1.57. 1.57 is the same as pi over 2, which is the same as we got from using the formula.
To write a sine function you simply need to use the following equation: f(x) = ASIN(bx + c) + d, where an is the amplitude, b is the period (you can find the period by dividing the absolute value b by 2pi. In your case, I believe the frequency and period are the same), c is the phase shift (or the shift along the x-axis
The period of a periodic function is the interval between two matching points on the graph. In other words, it's the distance along the x-axis that the function has to travel before it starts to repeat its pattern. The basic sine and cosine functions have a period of 2, while tangent has a period of.
If your trig function is either a tangent or cotangent, then you'll need to divide pi by the absolute value of your B. Our function, f(x) = 3 sin(4x + 2), is a sine function, so the period would be 2 pi divided by 4, our B value.
1:54 16:10 Suggested clip How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift YouTubeStart of suggested client of suggested clip How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift
0:03 2:07 Suggested clip Finding the Period and Amplitude of a Cosine Function — Quick YouTubeStart of suggested client of suggested clip Finding the Period and Amplitude of a Cosine Function — Quick
If a function has a repeating pattern like sine or cosine, it is called a periodic function. The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. So the period of or is. Any part of the graph that shows this pattern over one period is called a cycle.

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